Arithmetic vs. Geometric

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

Identify the common difference in the sequence: 5, 9, 13, ...

Back

The common difference is 4.

Front

Identify the common ratio in the sequence: 2, 6, 18, ...

Back

The common ratio is 3.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the common difference in the sequence: 97, 86, 75, 64, ...

Back

The common difference is -11.

Front

What is the common ratio in the sequence: -2, 4, -8, 16, ...

Back

The common ratio is -2.

Front

What are the next three terms in the geometric sequence: 512, 256, 128, ...?

Back

The next three terms are 64, 32, 16.

Front

What is the difference between arithmetic and geometric sequences?

Back

Arithmetic sequences have a constant difference between terms, while geometric sequences have a constant ratio.